Periodic Orbits of Hamiltonian Systems
主 题: Periodic Orbits of Hamiltonian Systems
报告人: Prof. Dr. E. Zehnder (ETH Zurich)
时 间: 2007-10-12 下午 2:00 - 3:00
地 点: 理科一号楼 1114(数学所活动)
The search for periodic solutions of Hamiltonian equations originated in celestial mechanics. It has given rise to many developments in mathematics. The Poincare - Birkhoff fixed point theorem, for example, inspired V. I. Arnold to formulate his conjectures about forced oscillations of Hamiltonian vector fields. Solutions of these conjectures led A. Floer to the Floer homology theories, a main tool in symplectic topology. In order to establish periodic solutions on a given energy surface, Paul Rabinowitz invented in the 1980-ties powerful variational technics. They allowed the construction of symplectic invariants which relate periodic orbits of Hamiltonian Systems to symplectic rigidity phenomena. More recently, the A. Weinstein conjecture about periodic orbits on contact type energy surfaces was studied by H. Hofer and others using PDE. methods of pseudoholomorphic curves. Nowadays these methods play an important role in the symplectic field theory, which, however is still under construction.
